Updated branching fraction measurements of $B^0_{(s)} \to K_{\mathrm{\scriptscriptstyle S}}^0 h^+ h^{\prime -}$ decays

The charmless three-body decays B$_{(s}_{)}^{0}$ → K$_{S}^{0}$ h$^{+}$ h$^{′ −}$ (where h$^{(′)}$ = π, K) are analysed using a sample of pp collision data recorded by the LHCb experiment, corresponding to an integrated luminosity of 3 fb$^{−1}$. The branching fractions are measured relative to that of the B$^{0}$ → K$_{S}^{0}$ π$^{+}$ π$^{−}$ decay, and are determined to be: $ \begin{array}{l}\frac{\mathrm{\mathcal{B}}\left({B}^0\to {K}_{\mathrm{S}}^0{K}^{\pm }{\pi}^{\mp}\right)}{\mathrm{\mathcal{B}}\left({B}^0\to {K}_{\mathrm{S}}^0{K}^{+}{\pi}^{-}\right)}=0.123\pm 0.009\left(\mathrm{stat}\right)\pm 0.015\left(\mathrm{syst}\right),\hfill \\ {}\frac{\mathrm{\mathcal{B}}\left({B}^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-}\right)}{\mathrm{\mathcal{B}}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.549\pm 0.018\left(\mathrm{stat}\right)\pm 0.033\left(\mathrm{syst}\right),\hfill \\ {}\frac{\mathrm{\mathcal{B}}\left({B}_s^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}{\mathrm{\mathcal{B}}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.191\pm 0.027\left(\mathrm{stat}\right)\pm 0.031\left(\mathrm{syst}\right)\pm 0.011\left({f}_s/{f}_d\right),\hfill \\ {}\frac{\mathrm{\mathcal{B}}\left({B}_s^0\to {K}_{\mathrm{S}}^0{K}^{\pm }{\pi}^{\mp}\right)}{\mathrm{\mathcal{B}}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=1.70\pm 0.07\left(\mathrm{stat}\right)\pm 0.11\left(\mathrm{syst}\right)\pm 0.10\left({f}_s/{f}_d\right),\hfill \\ {}\frac{\mathrm{\mathcal{B}}\left({B}_s^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-}\right)}{\mathrm{\mathcal{B}}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}\in \left[0.008-0.051\right]\kern0.5em \mathrm{at}\kern0.5em 90\%\kern0.5em \mathrm{confidence}\kern0.5em \mathrm{level},\hfill \end{array} $ where f$_{s}$ /f$_{d}$ represents the ratio of hadronisation fractions of the B$_{s}^{0}$ and B$^{0}$ mesons.